Numerical Solution of Partial Differential Equations

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/08 Numerical Analysis.

Examination method

Oral exam and assessment of laboratory work.

Learning
objectives

The course mainly concerns the study of methods and algorithms for the numerical solution of problems described by partial differential models. The main differential operators (elliptic, parabolic and hyperbolic) will be examined and, through the numerical and algorithmic analysis of the solution stages, the course aims to introduce students to the issues underlying the solution of application models.

Syllabus

Preliminary concepts and definitions on partial differential operators. Numerical solution of partial differential operators (elliptic, parabolic, hyperbolic), Finite difference method, Finite volume method. Level-set formulation in image analysis. Navier-Stokes equations in ocean circulation models.

Expected learning
outcomes

By the end of the course, students must demonstrate that they

understand and know the general issues relating to the analysis of methods for the numerical solution of partial differential operators;
are able to apply the knowledge acquired by independently designing numerical algorithms for numerical simulation models;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem relating to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Analysis of the issues addressed during the course on a case study. Independence in preparing the case study. Clarity of exposition.

Numerical Solution of Partial Differential Equations